Statistical properties of output from logarithmic quantizer

For the logarithmic quantizer, under the condition that the input of the quantizer is a continuous random variable, some statistical properties of the quantization output, such as probability density function, characteristic function and moments are analyzed in detail. Then if the input contains unknown parameters, the moment estimate of the parameters can be obtained based on the quantization output observations. Since finite logarithmic quantizer is more feasible in practice, the statistical properties of the output for such quantizer are also analyzed. Two examples are given to illustrate the methods proposed in this paper.

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